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Search: id:A036498
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| A036498 |
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Numbers of the form n*(6*n-1) and n*(6*n+1) for positive or negative n. |
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+0
3
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| 0, 5, 7, 22, 26, 51, 57, 92, 100, 145, 155, 210, 222, 287, 301, 376, 392, 477, 495, 590, 610, 715, 737, 852, 876, 1001, 1027, 1162, 1190, 1335, 1365, 1520, 1552, 1717, 1751, 1926, 1962, 2147, 2185, 2380, 2420, 2625, 2667, 2882, 2926, 3151, 3197, 3432, 3480
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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PartitionQ[ p ] is odd and contains an extra even partition; series term z^p in Product( 1-z^n, (n,1,oo) ) has coefficient (+1). - wouter.meeussen(AT)pandora.be
n such that the number of partitions of n into distinct parts with an even number of parts exceed by 1 the number of partitions of n into distinct parts with an odd number of parts.
In formal power series, A010815=(product(1-x^k),k>0), ranks of coefficients 1. (A001318=ranks of nonzero (1 or -1) in A010815=ranks of odds terms in A000009)
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FORMULA
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n(n+1)/6 for n=0 or 5 (modulo 6)
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MAPLE
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p1 := n->n*(6*n-1): p2 := n->n*(6*n+1): for n from 0 to 100 do printf(`%d, %d, `, p1(n), p2(n)) od:
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MATHEMATICA
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Table[ 1/8*(-1 + (-1)^k + 2*k)*(-3 + (-1)^k + 6*k), {k, 2, 64} ]
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PROGRAM
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(PARI) \ps 5000; for(n=1, 5000, if(polcoeff(eta(x), n, x)==1, print1(n, ", ")))
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CROSSREFS
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Cf. A000009, A001318, A036499, A010815. The union of A049452 and A049453.
Sequence in context: A049114 A030735 A084164 this_sequence A076409 A012863 A028281
Adjacent sequences: A036495 A036496 A036497 this_sequence A036499 A036500 A036501
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KEYWORD
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nonn
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AUTHOR
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wouter.meeussen(AT)pandora.be
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EXTENSIONS
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Better description from Claude Lenormand (claude.lenormand(AT)free.fr), Feb 12 2001
Additional comments and more terms from James A. Sellers (sellersj(AT)math.psu.edu), Feb 14 2001
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